This paper explores the topological signatures of ReLU neural network activation patterns. We consider feedforward neural networks with ReLU activation functions and analyze the polytope decomposition of the feature space induced by the network. Mainly, we investigate how the Fiedler partition of the dual graph and show that it appears to correlate with the decision boundary -- in the case of binary classification. Additionally, we compute the homology of the cellular decomposition -- in a regression task -- to draw similar patterns in behavior between the training loss and polyhedral cell-count, as the model is trained.

翻译：本文探讨了ReLU神经网络激活模式的拓扑特征。我们研究了具有ReLU激活函数的前馈神经网络，并分析了网络在特征空间诱导的多面体分解结构。重点考察了其对偶图的费德勒划分，并证明在二分类任务中该划分与决策边界存在显著相关性。此外，在回归任务中通过计算胞腔分解的同调群，揭示了模型训练过程中训练损失与多面体胞腔数量变化之间的行为相似性。